Spring
2017:
Numerical Methods for Differential Equations
Class Information:
Office Hour: by appointment
Office Location: 624 Pao Yue-Kong Library
email: lzhang2012 AT sjtu
TA Office Hour:
TA Office Location: Graduate office, 5th floor Pao Yue-Kong Library
email: ldfang.sjtu AT gmail.com
Homework online: Thursday in odd weeks
Homework due: Next Thursday in odd weeks in class
Homework：%10
Quiz: %10
Project: %20
Final: %60
Homework: (available before the
separator ||)
Homework 1,
Homework 2,
Homework 3,
Homework 4,
Homework 5,
Homework 6,
||
Homework 7,
Homework 8,
Exams:
Example Code in Julia:
Forward Euler:
euler_forward.jl.
Backward Euler:
euler_backward.jl,
newton4euler.jl.
Stability Region for RK methods:
stabilityregion.jl.
Stiff ODE:
stiffode.jl.
Example Code for Linear Advection Equation:
http://people.math.sfu.ca/~stockie/teaching/apma930/examples/linadv.m
Example Code for Burgers Equation:
https://people.sc.fsu.edu/~jburkardt/m_src/burgers_time_inviscid/burgers_time_inviscid.html
Project Topics:
1. The
(unfinished) PDE Coffee Table Book by
Lloyd N. Trefethen and Kristine Embree
2. MIT
Open Course, Mathematical Methods for Engineers II by
Gilbert Strang
3. Your research topic
References:
ODE and PDE:
A First Course in the Numerical Analysis of Differential Equations by Arieh Iserles
Finite
Difference Methods for Ordinary and Partial Differential Equations by
Randy LeVeque
ODE only:
Endre Suli's notes by
Endre Suli
For Geometric Integrator:
Hairer's lectures on geometric integration:
http://www.unige.ch/~hairer/poly_geoint/week1.pdf,
http://www.unige.ch/~hairer/poly_geoint/week2.pdf
Vilmart's animation:
http://www.unige.ch/~vilmart/java.html
For Conservation Laws:
Chi-Wang Shu's lectures on Numerical Methods for Hyperbolic Conservation Laws:
https://mathema.tician.de/dl/academic/notes/257/257.pdf
Spring
2017:
Numerical Methods for PDEs (math graduates)
Class Information:
Office Hour: by appointment
Office Location: 624 Pao Yue-Kong Library
email: lzhang2012 AT sjtu
TA Office Hour:
TA Office Location: 502 Pao Yue-Kong Library
email: liuxinliang@sjtu.edu.cn
Homework out: Monday
Homework due: Following Monday
Homework：%10
Quiz: %10
Project: %20
Final: %60
Lecture Notes:
Homework: (available before the
separator ||)
Homework 1,
Homework 2,
Homework 3,
Homework 4,
Homework 5,
Homework 6,
Homework 7,
Homework 8,
Homework Solution:
Solution 1,
Solution 2,
Solution 3,
Solution 4,
Quiz:
Quiz,
Solution of Quiz,
Exams:
Example Code:
5-point finite difference:
Laplacian.ipynb (run in Jupyter Notebook).
Syllabus:
References:
Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics 3rd Edition
by Dietrich Braess
有限元方法的数学基础, 王烈衡, 许学军, 科学出版社
The Mathematical Theory of Finite Element Methods (Texts in Applied Mathematics) by Susanne Brenner and Ridgway Scott
